100gm of an aq. solution of sugar contains 30% sugar by mass. How much water should be evaporated get 60% sugar solution by mass?

Explanation

To solve the problem, we need to determine how much water should be evaporated from a 100 g sugar solution that initially contains 30% sugar by mass in order to achieve a final concentration of 60% sugar by mass.

### Step-by-Step Solution:

1. **Identify the Initial Composition of the Solution:**
- The total mass of the solution is 100 g.
- The solution contains 30% sugar by mass.
- Therefore, the mass of sugar in the solution is:
\[ \text{Mass of sugar} = 30\% \text{ of } 100 \text{ g} = \frac{30}{100} \times 100 = 30 \text{ g} \]
- The mass of water in the solution is:
\[ \text{Mass of water} = 100 \text{ g} - 30 \text{ g} = 70 \text{ g} \]

2. **Determine the Final Composition of the Solution:**
- We want to achieve a solution that is 60% sugar by mass.
- Let \( x \) be the mass of water that needs to be evaporated.
- After evaporation, the mass of water will be:
\[ \text{Mass of water after evaporation} = 70 \text{ g} - x \]
- The total mass of the new solution will then be:
\[ \text{Total mass of new solution} = 30 \text{ g (sugar)} + (70 \text{ g} - x) \text{ g (water)} = 100 \text{ g} - x \]

3. **Set Up the Equation for the Final Concentration:**
- We want the final solution to be 60% sugar by mass, which gives us the equation:
\[ \frac{\text{Mass of sugar}}{\text{Total mass of new solution}} = 60\% \]
- Substituting the known values:
\[ \frac{30 \text{ g}}{100 \text{ g} - x} = 0.60 \]

4. **Solve for \( x \):**
- Cross-multiplying to eliminate the fraction:
\[ 30 = 0.60 \times (100 - x) \]
- Expanding the right side:
\[ 30 = 60 - 0.60x \]
- Rearranging the equation:
\[ 0.60x = 60 - 30 \]
\[ 0.60x = 30 \]
- Dividing both sides by 0.60:
\[ x = \frac{30}{0.60} = 50 \text{ g} \]

5. **Conclusion:**
- Therefore, the amount of water that should be evaporated to obtain a 60% sugar solution is **50 grams**.